Horizontal wells with continuous reservoir sections exceeding 10,000 ft are being used for the development of a number of oil fields, e.g. the laterally extensive low permeability chalk in the Dan/Halfdan oil accumulation as well as on a number of other fields located in the Danish part of the North Sea.
To avoid the risk of a hole collapse as a result of drilling, the wells are typically cased off with intermediate casings, including the reservoir section, denoted the pay zone. In wells with large pressure gradients along the well bore, a traditional completion strategy involves installation of a cemented liner with an inner string, the tubing, extending all the way to the surface. Operational experience has demonstrated that such an approach, known as the Perforate-Stimulate-Isolate (PSI) system, is costly and yields modest well productivity when wells are acid-stimulated below fracturing conditions.
EP 1 184 537 describes an improved method of stimulating a well referred to as the Controlled Acid Jet (CAJ) liner approach allowing stimulation of even very long horizontal well sections in a single operation. The CAJ liner is a non-cemented liner with a limited number of unevenly spaced holes (perforations) which ensures efficient acid stimulation of the complete reservoir section, provided the acid is pumped at sufficiently high rates to enable complete displacement of a mud phase built up along the bore hole walls. The article “Controlled Acid Jet Technique (CAJ) for Effective Single Operation Stimulation of 14,000+ ft Long Reservoir Sections”, by J. H. Hansen and N. Nederveen, SPE 78318, Paper presented at the SPE 13th European Petroleum Conference, Aberdeen, Scotland, 29-31 Oct. 2002, describes the CAJ liner concept in greater detail. CAJ liners can be installed in combination with traditional cemented liners or they can be deployed to cover the entire reservoir interval in case selective water shut-off is not mandatory.
The CAJ liner has, in several ways, set new standards for the completion and stimulation of long horizontal wells. One of the significant achievements with the CAJ liners is the remarkably effective acid coverage resulting from stimulation of long reservoir sections in a single operation. A typical CAJ liner length represents more than 20 times the interval length covered during matrix acid stimulation in a traditional cemented and perforated liner, completed with the PSI system. Furthermore, CAJ liners show consistently better productivity per unit reservoir length than cemented liners. In the Danish part of the North Sea, CAJ liners have to date been installed in more than 80 wells covering a perforated interval of some 650,000 ft.
During the stimulation of an oil well, making best possible use of the stimulation fluid and maximizing well productivity are matters of great importance. Consequently, it is desirable to model or simulate such stimulation processes so as to determine process parameters including suitable stimulation schedules that provide a good utilisation of the stimulation fluid and a high well productivity. Unfortunately such modelling and simulation require significant computational efforts, and an accurate simulation of the transient, i.e. time-dependant aspects of material flow in such systems is difficult to achieve.
There have been attempts to model the stimulation of wells, e.g. by employing an experimental approach such as the one described in “The Existence of an Optimum Damköhler Number for Matrix Stimulation of Carbonate Formations”, Fredd, C. N., Tjia, R. And Fogler, H. S. (1997). SPE 38167, where core flood results are used to predict an optimum pump rate. However, it remains uncertain how such approaches perform in practical field applications.
Furthermore, there have also been modelling attempts that incorporate reservoir properties but only under steady-state conditions, thus falling short to simulate transient behaviour. Finally, some time-dependent effects have been modelled but only for comparably small reservoir sections containing a cemented liner.